Application of the Gauss theorem to the study of silicic calderas: The calderas of La Primavera, Los Azufres, and Los Humeros (Mexico)

We explored applications (including limitations) of Gauss's theorem to the study of silicic calderas. First it enables us to determine the mass deficiency from calderas. Mass deficiency itself has also other potential applications. It enables to make qualitative comparisons between calderas. We can use the mass deficiency to test, in a quick way and as a preliminary step to a formal gravity inversion, for the feasibility of caldera types of simple geometry (i.e., piston subsidence and funnel models). This application can be done in a straightforward way, once the mass deficiency has been determined. For this purpose the mass deficiency is converted to the volume of material missing at the caldera. Subsequently, for example, this volume and the respective caldera diameter enable us to estimate the height of the cylinder fitting the piston subsidence model. If the obtained parameters are congruent with the known geology and geophysical information then the model may be considered further in the inversion of the gravity data for the detailed structure. Other simple models (i.e., the funnel model) can also be analyzed in this way. In particular, when working with a piston subsidence caldera type, the Gauss theorem enables us to estimate the caldera collapse (very difficult to obtain based on geologic information alone). These possible uses of Gauss's theorem are illustrated with the calderas of La Primavera, Los Azufres, and Los Humeros caldera (Mexico). The obtained mass deficiency from these calderas follow the linear mass deficiency-diameter trend observed for other calderas. In particular, because of their diameters and mass deficiencies, La Primavera and Krakatau calderas can be considered equiparable. This comparison is of the most importance considering that La Primavera is located in the neighbourhood of a metropolis (Guadalajara City). Since geophysical studies have already established a piston subsidence model for these calderas, we assessed Gauss's theorem used to estimate their collapses. The respective estimated subsidences for La Primavera (600 m), Los Humeros (500 m), and Los Azufres calderas (800 and 1200 m, respectively) are supported by borehole data. These relatively small subsidences, in relation to many calderas in western US, can be explained by the presence of cylindrical to sub-spherical magma chambers (of smaller size than those underlying the western US calderas-of Yellowstone, Valles, and Long Valley for example) in an epicontinental setting of young Quaternary rocks (against Precambrian cratonic basement in western US). A reassessment of all the available geological and geophysical information was also done. In particular, the caldera limits were checked and corrected when necessary based on available 2-D gravity modeling, gravity gradients, and the location of the volcanic vents. Regional tectonic lineaments might explain many of the particular details of their structures. La Primavera caldera might have formed through a piecemeal subsidence (controlled by the pre-caldera tectonics); Los Humeros caldera is an example of a caldera that evolved by incremental growth (as the Vulsiniani calderas in Italy). The Los Azufres caldera comprises two contiguous calderas emplaced in a regional tectonic depression.